Thermally regenerative electrochemical systems (TRES) are systems in which heat is converted into electricity in an electrochemical heat engine. The heat recovery strategy in TRES is based on the temperature dependence of the electrochemical potential of the system components. For the half reaction, A+n e−→B, the thermogalvanic coefficient α is defined as:
                    α        =                                            ∂              V                                      ∂              T                                =                                    Δ              ⁢                                                          ⁢                              S                                  A                  ,                  B                                                                    n              ⁢                                                          ⁢              F                                                          (        1        )            where V is the electrode potential, T is temperature, n is the number of electrons transferred in the reaction, F is Faraday's constant, and ΔSA,B is the partial molar entropy change for the half cell reaction at isothermal conditions. For the full cell reaction, A+B→C+D (discharge), the thermogalvanic coefficient α is defined as:
                    α        =                                            ∂              E                                      ∂              T                                =                                                    -                                  1                                      n                    ⁢                                                                                  ⁢                    F                                                              ⁢                                                                    ∂                    Δ                                    ⁢                                                                          ⁢                  G                                                  ∂                  T                                                      =                                          Δ                ⁢                                                                  ⁢                S                                            n                ⁢                                                                  ⁢                F                                                                        (        2        )            where E is the full cell voltage and ΔG and ΔS are the change of partial molar Gibbs free energy and partial molar entropy, respectively, in the full cell reaction.
Generally, the voltage of the electrochemical cell depends on temperature; thus, a thermodynamic cycle can be constructed by discharging the electrochemical cell at T1 and charging the electrochemical cell at T2. If the charging voltage at T2 is lower than the discharging voltage at T1, net energy is produced by the voltage difference, similar to a thermomechanical engine whose theoretical efficiency is limited by Carnot efficiency.
Traditional TRES are often impractical, as such systems must often be operated at conditions that are incompatible with many processes in which heat recovery would be useful. Improved systems and associated methods would be desirable.